【PyTorch基础教程1】线性模型(学不会来打我啊)

文章目录

  • 一、线性模型
  • 二、绘图工具
  • 三、作业
  • Reference

一、线性模型

不要小看简单线性模型哈哈,虽然这讲我们还没正式用到pytorch,但是用到的前向传播、损失函数、两种绘loss图等方法在后面是很常用的。
对下面的代码说明:

  • zip函数可以将x_datay_data组合元组列表,在for循环中每次遍历就是对于列表中的每个元组。
  • 函数forward()中,有一个变量w。这个变量最终的值是从for循环中传入的。
# -*- coding: utf-8 -*-
"""
Created on Tue Oct 12 14:30:13 2021

@author: 86493
"""
import numpy as np
import matplotlib.pyplot as plt

x_data = [1.0, 2.0, 3.0]
y_data = [2.0, 4.0, 6.0]

def forward(x):
    return x * w

def loss(x, y):
    y_pred = forward(x)
    return (y_pred - y) * (y_pred - y)

# 保存权重
w_list = []
# 保存权重的损失函数值
mse_list = []

# 穷举w值对应的损失函数MSE
for w in np.arange(0.0, 4.1, 0.1):
    print('w = ', w)
    loss_sum = 0
    for x_val, y_val in zip(x_data, y_data):
        # 为了打印y预测值,其实loss里也计算了
        y_pred_val = forward(x_val)
        loss_val = loss(x_val, y_val)
        loss_sum += loss_val
        print('\t', x_val, y_val,
              y_pred_val, loss_val)
    print('MSE = ', loss_sum / 3)
    print('='*60)
    w_list.append(w)
    mse_list.append(loss_sum / 3)
    

 # 绘loss变化图,横坐标是w,纵坐标是loss
plt.plot(w_list, mse_list)
plt.ylabel('Loss')
plt.xlabel('w')
plt.show()

【PyTorch基础教程1】线性模型(学不会来打我啊)_第1张图片

刚才对应的打印结果为:

w =  0.0
	 1.0 2.0 0.0 4.0
	 2.0 4.0 0.0 16.0
	 3.0 6.0 0.0 36.0
MSE =  18.666666666666668
============================================================
w =  0.1
	 1.0 2.0 0.1 3.61
	 2.0 4.0 0.2 14.44
	 3.0 6.0 0.30000000000000004 32.49
MSE =  16.846666666666668
============================================================
w =  0.2
	 1.0 2.0 0.2 3.24
	 2.0 4.0 0.4 12.96
	 3.0 6.0 0.6000000000000001 29.160000000000004
MSE =  15.120000000000003
============================================================
w =  0.30000000000000004
	 1.0 2.0 0.30000000000000004 2.8899999999999997
	 2.0 4.0 0.6000000000000001 11.559999999999999
	 3.0 6.0 0.9000000000000001 26.009999999999998
MSE =  13.486666666666665
============================================================
w =  0.4
	 1.0 2.0 0.4 2.5600000000000005
	 2.0 4.0 0.8 10.240000000000002
	 3.0 6.0 1.2000000000000002 23.04
MSE =  11.946666666666667
============================================================
w =  0.5
	 1.0 2.0 0.5 2.25
	 2.0 4.0 1.0 9.0
	 3.0 6.0 1.5 20.25
MSE =  10.5
============================================================
w =  0.6000000000000001
	 1.0 2.0 0.6000000000000001 1.9599999999999997
	 2.0 4.0 1.2000000000000002 7.839999999999999
	 3.0 6.0 1.8000000000000003 17.639999999999993
MSE =  9.146666666666663
============================================================
w =  0.7000000000000001
	 1.0 2.0 0.7000000000000001 1.6899999999999995
	 2.0 4.0 1.4000000000000001 6.759999999999998
	 3.0 6.0 2.1 15.209999999999999
MSE =  7.886666666666666
============================================================
w =  0.8
	 1.0 2.0 0.8 1.44
	 2.0 4.0 1.6 5.76
	 3.0 6.0 2.4000000000000004 12.959999999999997
MSE =  6.719999999999999
============================================================
w =  0.9
	 1.0 2.0 0.9 1.2100000000000002
	 2.0 4.0 1.8 4.840000000000001
	 3.0 6.0 2.7 10.889999999999999
MSE =  5.646666666666666
============================================================
w =  1.0
	 1.0 2.0 1.0 1.0
	 2.0 4.0 2.0 4.0
	 3.0 6.0 3.0 9.0
MSE =  4.666666666666667
============================================================
w =  1.1
	 1.0 2.0 1.1 0.8099999999999998
	 2.0 4.0 2.2 3.2399999999999993
	 3.0 6.0 3.3000000000000003 7.289999999999998
MSE =  3.779999999999999
============================================================
w =  1.2000000000000002
	 1.0 2.0 1.2000000000000002 0.6399999999999997
	 2.0 4.0 2.4000000000000004 2.5599999999999987
	 3.0 6.0 3.6000000000000005 5.759999999999997
MSE =  2.986666666666665
============================================================
w =  1.3
	 1.0 2.0 1.3 0.48999999999999994
	 2.0 4.0 2.6 1.9599999999999997
	 3.0 6.0 3.9000000000000004 4.409999999999998
MSE =  2.2866666666666657
============================================================
w =  1.4000000000000001
	 1.0 2.0 1.4000000000000001 0.3599999999999998
	 2.0 4.0 2.8000000000000003 1.4399999999999993
	 3.0 6.0 4.2 3.2399999999999993
MSE =  1.6799999999999995
============================================================
w =  1.5
	 1.0 2.0 1.5 0.25
	 2.0 4.0 3.0 1.0
	 3.0 6.0 4.5 2.25
MSE =  1.1666666666666667
============================================================
w =  1.6
	 1.0 2.0 1.6 0.15999999999999992
	 2.0 4.0 3.2 0.6399999999999997
	 3.0 6.0 4.800000000000001 1.4399999999999984
MSE =  0.746666666666666
============================================================
w =  1.7000000000000002
	 1.0 2.0 1.7000000000000002 0.0899999999999999
	 2.0 4.0 3.4000000000000004 0.3599999999999996
	 3.0 6.0 5.1000000000000005 0.809999999999999
MSE =  0.4199999999999995
============================================================
w =  1.8
	 1.0 2.0 1.8 0.03999999999999998
	 2.0 4.0 3.6 0.15999999999999992
	 3.0 6.0 5.4 0.3599999999999996
MSE =  0.1866666666666665
============================================================
w =  1.9000000000000001
	 1.0 2.0 1.9000000000000001 0.009999999999999974
	 2.0 4.0 3.8000000000000003 0.0399999999999999
	 3.0 6.0 5.7 0.0899999999999999
MSE =  0.046666666666666586
============================================================
w =  2.0
	 1.0 2.0 2.0 0.0
	 2.0 4.0 4.0 0.0
	 3.0 6.0 6.0 0.0
MSE =  0.0
============================================================
w =  2.1
	 1.0 2.0 2.1 0.010000000000000018
	 2.0 4.0 4.2 0.04000000000000007
	 3.0 6.0 6.300000000000001 0.09000000000000043
MSE =  0.046666666666666835
============================================================
w =  2.2
	 1.0 2.0 2.2 0.04000000000000007
	 2.0 4.0 4.4 0.16000000000000028
	 3.0 6.0 6.6000000000000005 0.36000000000000065
MSE =  0.18666666666666698
============================================================
w =  2.3000000000000003
	 1.0 2.0 2.3000000000000003 0.09000000000000016
	 2.0 4.0 4.6000000000000005 0.36000000000000065
	 3.0 6.0 6.9 0.8100000000000006
MSE =  0.42000000000000054
============================================================
w =  2.4000000000000004
	 1.0 2.0 2.4000000000000004 0.16000000000000028
	 2.0 4.0 4.800000000000001 0.6400000000000011
	 3.0 6.0 7.200000000000001 1.4400000000000026
MSE =  0.7466666666666679
============================================================
w =  2.5
	 1.0 2.0 2.5 0.25
	 2.0 4.0 5.0 1.0
	 3.0 6.0 7.5 2.25
MSE =  1.1666666666666667
============================================================
w =  2.6
	 1.0 2.0 2.6 0.3600000000000001
	 2.0 4.0 5.2 1.4400000000000004
	 3.0 6.0 7.800000000000001 3.2400000000000024
MSE =  1.6800000000000008
============================================================
w =  2.7
	 1.0 2.0 2.7 0.49000000000000027
	 2.0 4.0 5.4 1.960000000000001
	 3.0 6.0 8.100000000000001 4.410000000000006
MSE =  2.2866666666666693
============================================================
w =  2.8000000000000003
	 1.0 2.0 2.8000000000000003 0.6400000000000005
	 2.0 4.0 5.6000000000000005 2.560000000000002
	 3.0 6.0 8.4 5.760000000000002
MSE =  2.986666666666668
============================================================
w =  2.9000000000000004
	 1.0 2.0 2.9000000000000004 0.8100000000000006
	 2.0 4.0 5.800000000000001 3.2400000000000024
	 3.0 6.0 8.700000000000001 7.290000000000005
MSE =  3.780000000000003
============================================================
w =  3.0
	 1.0 2.0 3.0 1.0
	 2.0 4.0 6.0 4.0
	 3.0 6.0 9.0 9.0
MSE =  4.666666666666667
============================================================
w =  3.1
	 1.0 2.0 3.1 1.2100000000000002
	 2.0 4.0 6.2 4.840000000000001
	 3.0 6.0 9.3 10.890000000000004
MSE =  5.646666666666668
============================================================
w =  3.2
	 1.0 2.0 3.2 1.4400000000000004
	 2.0 4.0 6.4 5.760000000000002
	 3.0 6.0 9.600000000000001 12.96000000000001
MSE =  6.720000000000003
============================================================
w =  3.3000000000000003
	 1.0 2.0 3.3000000000000003 1.6900000000000006
	 2.0 4.0 6.6000000000000005 6.7600000000000025
	 3.0 6.0 9.9 15.210000000000003
MSE =  7.886666666666668
============================================================
w =  3.4000000000000004
	 1.0 2.0 3.4000000000000004 1.960000000000001
	 2.0 4.0 6.800000000000001 7.840000000000004
	 3.0 6.0 10.200000000000001 17.640000000000008
MSE =  9.14666666666667
============================================================
w =  3.5
	 1.0 2.0 3.5 2.25
	 2.0 4.0 7.0 9.0
	 3.0 6.0 10.5 20.25
MSE =  10.5
============================================================
w =  3.6
	 1.0 2.0 3.6 2.5600000000000005
	 2.0 4.0 7.2 10.240000000000002
	 3.0 6.0 10.8 23.040000000000006
MSE =  11.94666666666667
============================================================
w =  3.7
	 1.0 2.0 3.7 2.8900000000000006
	 2.0 4.0 7.4 11.560000000000002
	 3.0 6.0 11.100000000000001 26.010000000000016
MSE =  13.486666666666673
============================================================
w =  3.8000000000000003
	 1.0 2.0 3.8000000000000003 3.240000000000001
	 2.0 4.0 7.6000000000000005 12.960000000000004
	 3.0 6.0 11.4 29.160000000000004
MSE =  15.120000000000005
============================================================
w =  3.9000000000000004
	 1.0 2.0 3.9000000000000004 3.610000000000001
	 2.0 4.0 7.800000000000001 14.440000000000005
	 3.0 6.0 11.700000000000001 32.49000000000001
MSE =  16.84666666666667
============================================================
w =  4.0
	 1.0 2.0 4.0 4.0
	 2.0 4.0 8.0 16.0
	 3.0 6.0 12.0 36.0
MSE =  18.666666666666668
============================================================

二、绘图工具

在深度学习中,我们一般没有打印上面这种loss图(一般横坐标为epoch,而上面这种图可以用于检测最优超参数是多少),下图这里loss虽然随着epoch增大而减少,但是在开发集上的效果却可能是先减小后增大的,所以应该找中间这个画竖线的点。

PS:可以学习模型训练可视化visdom工具,训练还要注意存盘的问题(如防止要训练7天,但在第6天报错了)。
【PyTorch基础教程1】线性模型(学不会来打我啊)_第2张图片
画图除了用matplotlib.pyplot,还经常使用pandas的dataframe.plot,如下:

# 增加loss折线图
import pandas as pd
df = pd.DataFrame(columns = ["Loss"]) # columns列名
df.index.name = "Epoch" 
for epoch in range(1, 201):
    loss = train()
    #df.loc[epoch] = loss.item()
    df.loc[epoch] = loss.item()
df.plot() 

上面这种loss图也是最典型的.

三、作业

实现线性模型( y = w x + b y=wx+b y=wx+b)并输出loss的3D图像。
【PyTorch基础教程1】线性模型(学不会来打我啊)_第3张图片

# -*- coding: utf-8 -*-
"""
Created on Tue Oct 12 17:04:46 2021

@author: 86493
"""
import numpy as np
import matplotlib.pyplot as plt;
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm

x_data = [1.0, 2.0, 3.0]
y_data = [2.0, 4.0, 6.0]

# 线性模型,多了个b
def forward(x,w,b):
    return x * w + b

# 损失函数,此处没变
def loss(x, y, w, b):
    y_pred = forward(x, w, b)
    return (y_pred - y) * (y_pred - y)

# 单独写出mse函数,为了计算不同w和b情况下对应的mse
def mse(w,b):
    l_sum = 0
    for x_val, y_val in zip(x_data, y_data):
        y_pred_val = forward(x_val,w,b)
        loss_val = loss(x_val, y_val,w,b)
        l_sum += loss_val
        print('\t', x_val, y_val, y_pred_val, loss_val)
    print('MSE=', l_sum / 3)
    return  l_sum/3

#迭代取值,计算每个w取值下的x,y,y_pred,loss_val
mse_list = []


# 画图

# 1.定义网格化数据
b_list=np.arange(-30,30,0.1)
w_list=np.arange(-30,30,0.1);

# 2.生成网格化数据
xx, yy = np.meshgrid(b_list, w_list, sparse=False, indexing='xy')

# 3.每个点的对应高度
zz=mse(xx,yy)

fig = plt.figure()
ax = Axes3D(fig)
ax.plot_surface(xx, yy, zz, 
                rstride=1,   # rows stride 指定行的跨度为1,只能是int
                cstride=1,   # columns stride 指定列的跨度为1
                cmap=cm.viridis) # 设置曲面的颜色
plt.show()

【PyTorch基础教程1】线性模型(学不会来打我啊)_第4张图片

Reference

[1] 3D图绘制:https://matplotlib.org/stable/tutorials/toolkits/mplot3d.html
[2] https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid
[3] Matplotlib3D作图-plot_surface(), .contourf(), plt.colorbar()
[4]【matplotlib】如何进行颜色设置选择cmap
[5] https://blog.csdn.net/Pin_BOY/article/details/119707358
[6] http://biranda.top/archives/page/2/

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